It is indeed an interaction between Ima::DBI's use
of prepare_cached and SQLite's changed error.
Invalidating the $dbh->{CachedKids} is a passable
work-around. I tried and failed to globally
turn caching off in Ima::DBI::set_sql, but that
probably would have caused performance issues anyway.
I'm still not sure exactly which change revealed this
problem.

DBD::SQLite seems to be the correct place to address this
issue.
Does anyone else have an opinion on that matter?
Is there a better forum for
DBD::SQLite discussions? The only other seems to be RT.

The dbi-users@perl.org mailing list is an appropriate place to discuss changes to DBDs and the most likely place other than rt.cpan.org for DBD authors to see your suggestions. Also, there may be similar issues with other DBDs so posting to the list might pull in some other ideas.